In this fourth paper of the series, we use the parametrized, spherically symmetric explosion method PUSH to perform a systematic study of two sets of non-rotating stellar progenitor models. Our study includes pre-explosion models with metallicities Z=0 and Z=Z$_{odot}times 10^{-4}$ and covers a progenitor mass range from 11 up to 75 M$_odot$. We present and discuss the explosion properties of all models and predict remnant (neutron star or black hole) mass distributions within this approach. We also perform systematic nucleosynthesis studies and predict detailed isotopic yields as function of the progenitor mass and metallicity. We present a comparison of our nucleosynthesis results with observationally derived $^{56}$Ni ejecta from normal core-collapse supernovae and with iron-group abundances for metal-poor star HD~84937. Overall, our results for explosion energies, remnant mass distribution, $^{56}$Ni mass, and iron group yields are consistent with observations of normal CCSNe. We find that stellar progenitors at low and zero metallicity are more prone to BH formation than those at solar metallicity, which allows for the formation of BHs in the mass range observed by LIGO/VIRGO.
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